So, they are not running on the same protocol. So the two blockchains are not the same, since they have to run on different protocols.
Yes, you got it now.
The good working of the protocol depends heavily on the behavior of its human players, about which nothing can be proved mathematically. It assumes that a majority of the players will be driven by immediate greed, and therefore would choose alternative X over Y when considering many specific choices that have been considered when designing the protocol. However, that assumption is not certain, and the possible situations and choices that the players may face is not bounded.
That is factually not true (aka a lie). Anyone with interest (=money, principle) in bitcoin is not driven by immediate greed. We had several price run ups followed by burst (bubble), and it is still alive (bitcoin), so "immediate greed" is not the long time motivator.
The protocol assumes, for example, that enough miners will choose to include transactions that have a significant fee, because they would get more money that way. It assumes that a majority of miners will choose to work on extending the longest chain rather than an orphaned branch, because they would want to maximize their chances of colelcting block rewards. And so on. Those assumptions follow from the basic assumption that most miners will want to maximize their immediate gain. Take away this assumption, and the other assumptions are no longer reasonable.
For example, suppose that some hacker manages to steal the remaining 44 k BTC from the USMS, and the US government threatens to criminalize bitcoin. American bitcoiners, and investors in bitcoin enterprises in the US, may decide "spontaneously", "for the good of bitcoin", to rewind the blockchain, with a hard fork if needed, to a point before that transaction. IF such a situation were to develop, would bitcoiners in the rest of the world agree to the fork?
Also, any change in the protocol is seriously wetted and reviewed by the community, and must be beneficial to the majority, else it would not be implemented by the majority, and would fail (it is still a conscensus mechanism, means majority of participants = consensus)
That is simply not true. Anyone can create a hard fork at any moment, without consulting (or even telling) anyone else. Those miners who like the change (that may be just a cosmetic one, just enough to distinguish the two versions) can switch, those who do not like it can stick to the old version. Exchanges and processors can opt for either version, or handle both as two separate cryptocoins. Users can use either, or both, or switch back and forth between them at any time, without losing the coins that they have in the other.
A cartel of miners holding the majority of the hashpower could, if they wanted to, pick one branch and make the other branch unusable by "jamming" it. But that is a separate "FUD". Other than that, nothing requires or creates a consensus, before or after the fork, and a majority that chooses one branch cannot prevent a minority from going the other way. Self-interest
may cause most miners to converge to one branch and abandon the other, but that convergence (unlike the majority-based consensus mechanism that operates within each chain) is not built into the protocol. The two clones may well survive, like any two independent cryptocoins.
You presume that people would act against their own known self interest in the number of millions
Yes, BECAUSE IT HAS ALREADY HAPPENED and IS EXPECTED TO HAPPEN AGAIN (except that I don't think that there are "millions" of bitcoiners who would have to be aware of a hard fork).
In the OP_MUL fork, hundreds of tousands of bitcoiners forgot their
immediate self-interest, and agreed to grossly violate the protocol by rewinding the blockchain -- because of longer-term interest. (AFAIK, the miners who had mined the discarded blocks lost their rewards, but presumably agreed to the rewinding nonetheless.)
EDIT: I see that I did use "fair" when I said that the difficulty had to be adjusted to maintain a "fair rate". "Fair" in the sense of "acceptably high", e.g. 1 block every 30 minutes rather than 1 block every year. Not "fair" in the sense of "just", "equitable", etc.